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Abstract
It is well known that pulsed laser can easily generate breakdown plasmas when the beam is focused. The laser-based gas breakdown phenomenon is caused by multiphoton ionization (MPI) and cascade ionization (CI) in a high-intensity electric field near the focal region. However, the phenomenon is complicated because it is affected by the purity of the gas and the focusing quality of the laser and optical systems. For a comprehensive understanding of the laser-induced breakdown phenomenon, the influence of an electric field on the threshold intensity of the laser-induced breakdown was investigated. The applied field disperses electrons generated in the focal area by the intense laser field, thereby increasing the laser-induced breakdown threshold intensity. The observed phenomenon is explained by a simple electron balance model.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
It is well known that breakdown plasma can be formed in a gas, on a solid surface and in transparent materials, by focusing pulsed laser radiation. The laser-induced breakdown phenomenon is widely used, for example in laser breakdown spectroscopy (LIBS) [1–3], laser ignition [4–6], and laser-triggered spark gap switches for pulsed power technologies [7,8]. Numerous studies have been conducted on the process involved in laser breakdown plasma formation [9]. Basically, it is considered that the laser-based gas breakdown phenomenon is caused by multiphoton ionization (MPI) and cascade ionization (CI) in a high-intensity electric field formed by focusing a pulsed laser.
Tambay et al. investigated the dependence of the laser breakdown threshold intensity on the laser wavelength and focusing diameter using an Nd: YAG laser [10]. They showed that the threshold intensity increases as the diameter of the focused beam decreases, and this behavior was explained by the effect of electron diffusion from the focal region. Davis et al. investigated the laser wavelength and pressure dependence of the laser breakdown threshold using an Nd: YAG laser, and compared their results with previous experimental results. These dependencies were determined over a wide range of parameters, and the observed thresholds reproduced the previous data within the range of a factor of 4 [11]. Based on the experimental results obtained by Davis, Gamal et al. investigated the breakdown threshold of N2 using Boltzmann simulations [12]. They showed that the breakdown threshold could be explained by a combination of MPI and CI; and further, that the experimentally observed increase in the breakdown threshold of the 3rd harmonic of the YAG laser could be explained by the effect of the vibrationally excited state of nitrogen molecules on the electron distribution function. Thiyagarajan et al. measured the laser breakdown threshold at 1064 nm in detail, and showed that the laser breakdown process at 1064 nm requires the correction of MPI in the main CI breakdown process [13]. They also reported the effect of micro-particles on the breakdown. Recently, Wu et al. succeeded in directly measuring the number of electrons leading to breakdown, using coherent microwave scattering [14]. They showed that the growth in the number of electrons leading to breakdown was owing to the CI caused by a 1064-nm Nd: YAG laser, along with the temporal increase in the second harmonic wave due to the MPI process.
It is considered that plasma or gas heating by means of laser electric fields with CI is mainly the result of inverse bremsstrahlung [15]. Recently, the inverse bremsstrahlung process has gained attention as an elementary process involving electron scattering by ions or atoms in a laser field [16].
Moreover, the recent development of the micro-chip laser has enabled output of the laser pulse width in a ‘pulse gap’ region, which lies between picosecond mode-locked laser output and nanosecond Q-switched laser output. Lim et al., investigated the pulse width dependence of the laser breakdown threshold in detail using a the variable pulse-width microchip laser [17], and reported that the conventional MPI and CI models could not explain the observed breakdown threshold dependence on pulse width. More detailed studies on the breakdown process are needed to interpret the recent results.
In [7], a combination of electric field with laser breakdown was utilized to form a laser trigger spark gap switch, which takes advantage of the fact that the discharge breakdown voltage between the electrodes can be lowered by forming laser breakdown plasma in the space where the electric field is applied. In addition, Takahashi et al. showed that by creating a laser-induced breakdown between electrodes to which a voltage was applied, a long-distance discharge could be generated, which could improve the ignition and combustion characteristics of a flammable premixture [18]. It was previously reported that, in an experiment in which a CO2 laser was focused into low-pressure air to form breakdown plasma, the formation of laser breakdown was suppressed by applying a voltage [19]. In that study, the CO2 laser was focused in 20 Torr air, and nearly 100% breakdown was formed without applying an electric field; but when a 600 V/cm electric field was applied, the breakdown could be largely suppressed. This phenomenon was explained by a model in which the initial electrons required for breakdown formation were drifted, by the electric field, from the focusing region of the laser. However, the CO2 laser has a long wavelength and low photon energy, meaning that MPI is less likely to occur, and there was considerable diffusion of electrons in that low pressure experiment, so the conditions differed greatly from experiments generating breakdown plasma using an Nd: YAG laser under atmospheric pressure.
In order to gain a comprehensive understanding of the laser breakdown process near atmospheric pressure using an Nd:YAG laser, the present study, for the first time, demonstrated changes in the breakdown threshold by applying an electric field on a nanosecond time scale near the focal point of a 1064-nm Nd: YAG laser. In the laser breakdown formed by focusing the Nd: YAG laser pulse in atmospheric air, an increase in the breakdown threshold intensity was observed when an electric field was applied. The focused spot size of the laser beam is an important parameter for evaluating this phenomenon; thus, this was measured in detail, and a 0-dimensional model of electron number growth was compared with the experimental results.
2. Experimental setup
Figure 1 shows the experimental setup for investigating the effect of the electric field on the laser breakdown phenomenon. The breakdown experiment was carried out in a chamber equipped with electrodes. The beam diameter of a laser pulse with a fundamental wavelength and pulse width of 6 ns, output from a flash lamp-excited Nd: YAG laser (Lotis TII LS-2132UT), was magnified 1.5 times from its original 6 mm, by a telescope with two lenses (focal lengths: 600 mm and 900 mm, respectively). The laser was focused on the center of the chamber by a lens with a focal length of 100 mm, to generate breakdown. The incident laser energy was measured by a laser energy sensor (Gentec ED-200), along with a quartz wedge, and the laser energy transmitted through the chamber was measured by another energy sensor (Ophir PE50BF), with a sensing region diameter of 46 mm. The temporal waveform of the transmitted laser light was measured by a photo-diode (Thorlabs: PDA10A), and the signal was recorded with an oscilloscope (Tektronix: MDO3054 500 MHz 2.5 GHz/s). However, as the frequency bandwidth of the photo-diode (150 MHz) was insufficient for measuring optical signals capable of reproducing the original laser beam waveform, the waveform measurement was only used as a reference. When the incident laser energy is adjusted using the flash lamp energy, the thermal lens effect may change the beam profile. Thus, the laser intensity was controlled by adjusting the angle of the half-wave plate in a combination half-wave plate and polarizer. A Faraday rotator (FR) was installed to prevent damage to the laser from the reflected laser light. The flash lamp was operated at 15 Hz, and a single-shot Q-switch signal was used to trigger the laser beam.
Fig. 1. Experimental setup for evaluating the effect of electric field on the laser-induced breakdown process.
In the center of the chamber, spherical electrodes with a radius of curvature of 4.5 mm were installed at 1.8 mm intervals. Spherical electrodes were used to avoid the electrode edge effect. A nearly uniform electric field was formed near the focal point. The laser breakdown was formed at the center of the gap of the spherical electrodes. A pulsed high-voltage output was generated by a DC high-voltage generator (Matsusada Precision: HGR30-25P), with high-voltage switching provided by a MOSFET (Behlke: HTS-301-GSM). The temporal high-voltage waveform was measured with a high-voltage probe (Tektronix P6015-A).
For the most part, high purity air (TAIYO NIPPON SANSO: G3 grade) was steadily supplied from a gas bottle, at 1 L/min, with a mass flow controller. Since the volume of the container was only 100 cm3, the air in the chamber was rapidly replaced.
The focused profile of the laser beam was evaluated by a beam profiler (Edmund Optics EO beam profiler). The actual laser breakdown was formed using a lens with a focal length of 100 mm, but since the focusing diameter was less than the minimum size required by the profiler, we evaluated the focused profile using a lens with a focal length of 300 mm. The measured beam profile, x-axis cross section, and y-axis cross section are shown in Figs. 2(a), 2(b), and 2(c), respectively. Since the average 1/e2 diameter (i.e., the Gaussian-fitted diameter at 1/e2 intensity) was 92.4 µm, the focused spot diameter in the laser breakdown experiment was evaluated to be 30.8 µm, given the focal length difference. The peak intensity of the laser beam was calculated assuming a Gaussian distribution. The Rayleigh length, corresponding to the length of the focal region, was 0.5 mm.
Fig. 2. Laser focused spot profile using an f = 300 mm plano-convex lens, observed by a laser beam profiler: (a) observed image with cross line and 1/e2 diameter, (b) cross section for the x-direction, (c) cross section for the y-direction
The experiment was conducted using the following procedure. In order to eliminate the influence of the residual charge from the previous breakdown experiment, the inside of the chamber was evacuated with a vacuum pump, then filled with air, and the laser beam was injected while the air was flowing at a rate of 1 L/min. A high voltage was applied by giving a signal to the MOSFET switch at the same time as the Q-switch signal was given to the laser. The incident and output energy of the laser were recorded, and the formation of breakdown was determined by the difference in the input and output energy.
3. Results
Figure 3 shows the dependence of the transmitted output energy on the laser incident energy. The estimated focusing intensity is shown on the upper x-axis of the figure. The blue triangles represent the data acquired when no electric field was applied. Since the input and output energies are the same until an incident energy of 17 mJ, we can see that breakdown does not occur until this point. However, when the incident energy exceeds 17 mJ, the output laser energy becomes significantly less than the incident energy, showing breakdown formation. This difference may be due to the energy of the laser being absorbed by the plasma or refracted beyond the area of the energy sensor.
Fig. 3. Relation between incident and output laser pulse energy with and without applied voltage of 1900 V, in air.
The data points for the case with applied voltage of 1900 V between the electrodes are indicated by red circles, with the open and filled circles indicating, respectively, the presence and non-presence of observed current flow between the electrodes. In the low-energy region, the incident and output laser energy values increase linearly, as in the case without the electric field, and this linear relationship is maintained until an incident energy of roughly 22.5 mJ, with breakdown occurring at higher laser energy values. Although there are some data points where breakdown occurs at low incident energy, the breakdown threshold is obviously higher with than without the electric field.
Figure 4 shows the results for the case with an applied voltage of 1000 V. As in Fig. 3, breakdown does not occur at low incident laser energy. Although the number of trials was small, the breakdown threshold energy without applied electric field was near 15 mJ, a similar value to that of the previous experiment. The threshold laser energy with applied electric field increases to 19 mJ.
Fig. 4. Relation between incident and output laser pulse energy with and without applying voltage of 1000 V, in air.
Figure 5 shows the applied voltage and laser waveforms observed by the photo-diode. The red line shows that the applied voltage waveform has a 200-ns pulse width and rise time of approximately 75 ns. The solid line shows the case without current being generated between the electrodes, and the broken line shows the case with current flow. The observed difference is the result of laser breakdown formation. As noted in Section 2, the photo-diode signal (blue line) does not reproduce the laser waveform precisely, but it can be seen that the latter half of the pulse is suppressed by the breakdown.
The laser breakdown threshold energy was evaluated at various applied voltages. In previous studies [10,11], the laser breakdown threshold was determined by visual or photo-diode detection of light emission from the breakdown plasmas. In the present study, however, since the breakdown emission could not be observed from the side, due to the electrode and gas supply, the evaluation was performed based on the graph data points at which the output energy decreased significantly from the input energy, as described above. The threshold was defined by the second largest energy in the breakdown data points, to eliminate variations in the small number of trials. Figure 6 shows the dependence of the output energy threshold on the applied voltage. When no electric field was applied, laser breakdown occurred at an incident energy of about 15 mJ (blue square data point). The threshold energy increased with increasing applied voltage up to 1500 V; but at higher voltages, it showed constant or slightly decreasing behavior.
To investigate the effect of gas species, an experiment using nitrogen was also conducted. Figure 7 shows the results of a similar evaluation of the breakdown threshold energy using pure nitrogen gas. The purity of the nitrogen was the same as the air. In this experiment, the breakdown threshold was also increased by applying an electric field. The breakdown threshold energy was about 15 mJ without applied voltage, but increased to 19 mJ with the application of 1900 V. The values in nitrogen were slightly lower than in air, with the same 1900 V application.
Fig. 7. Relation between incident and output laser pulse energy with and without applied voltage of 1900 V, in nitrogen.
4. Discussion
The breakdown threshold intensity observed in this experiment agrees with the values reported by Davis et al. [11] and Tambay [10] et al.. Regarding the difference in the kind of gas, the breakdown threshold energy in air (Fig. 3) and in nitrogen (Fig. 7) did not differ greatly. If the initial electrons are generated by multiphoton ionization of oxygen or nitrogen molecules, it is considered that air containing oxygen with a low ionization potential exhibits a lower breakdown threshold energy than pure nitrogen. Therefore, the laser breakdown here was not initiated by multiphoton ionization of oxygen but by impurities in the gas. Davis et al. also noted that the initial electron supply is due to impurities [11]. According to the gas manufacturer, the purity of the gas used in this experiment may contain less than 1 ppm of hydrocarbons. The focusing volume can be estimated as $7 \times {10^{ - 7}}$ cm3 from the laser focused spot diameter and the Rayleigh length. Therefore, since there are as many as $1.8 \times {10^{13}}$ hydrocarbons in this volume, it is considered that the initial electrons were supplied by the ionization of those impurities with low ionization energy. However, it is not known what kind of hydrocarbon impurities were in the gas.
To investigate the increase in the breakdown threshold energy with applied voltage, we considered the following 0-dimensional model:
Since the breakdown threshold energy without applied voltage was approximately 15 mJ, the breakdown occurs when α exceeds approximately $1 \times {10^9}$ [1/sec]. Thus, we can determine the dependence of the breakdown threshold for the case with applied voltage by considering the effective electron multiplication factor with the drift loss. This dependence is shown in Fig. 9 as the solid blue line. The increase in breakdown threshold energy varies from several mJ to several tens of mJ with the application of the electric field. The experimental results shown in Fig. 6 are also plotted in this figure. The model prediction coincides well with the results of the low-voltage experiments. However, in the experiment, there was a tendency for peak or saturation to occur at an applied voltage of 1500 V, but in the model the breakdown threshold energy increases monotonically with the applied voltage.
Fig. 9. Threshold breakdown energy dependence on applied voltage using the 0-dimensional model (solid line). Experimental data points are also plotted on the figure.
The model is a relatively simple means of conceiving the increase in the breakdown threshold as a result of the application of an electric field, and some physics has not been taken into consideration. For example, Bolsig+ employs a Boltzmann simulation for second order approximation. Pitchford et al. showed the formation of high-energy electron components in their simulation, using a Boltzmann simulation with 6-term approximation [21]. Gamal et al. noted the effect of multiphoton ionization on the metastable state of nitrogen in the early stage of breakdown, using a 1064-nm laser [12].
It is also necessary to consider the effect of electric field shielding by the plasma. The electric field is decomposed into an electric field induced by an external electric field and plasma: E = Eext - Eind, with Eext and Eind being the external and induced fields, respectively. Eind increases with increasing electron density. Assuming that the external electric field is shielded by uniform dielectric polarization, the magnitude of the polarization electric field can be calculated from Gauss’ law, as ${E_{ind}}/d = en/{\epsilon }$. Thus, the electron density required for shielding the external field is $n = {\epsilon }E/ed$. Assuming the external electric field to be 1 MV/m and d = 30 µm, the electron density for shielding the external field is calculated to be $n\; = \; 1.8 \times {10^{18}}$ m-3. Thus, the electron density becomes in the order of 1012 cm-3 and Eind is comparable to Eext. This may cause saturation of the breakdown threshold energy with applied voltage.
The study revealed that the laser breakdown process, which exhibits an electron density increase of several tens of orders of magnitude and progresses on a nanosecond time scale, can be influenced by the application of an electric field, meaning that a controllable loss term can be applied to the laser breakdown process. Utilizing this method with various lasers and focusing conditions is expected to lead to a comprehensive understanding of the laser breakdown process.
5. Conclusion
It was shown that the breakdown threshold of the laser breakdown plasma formed by focusing the fundamental wave of an Nd: YAG laser in atmospheric pressure air was increased by the application of an electric field. Comparison of the gas species results suggested that multiphoton ionization due to breakdown is caused by impurities in the gas. The constructed 0-dimensional model could qualitatively explain the increase in the breakdown threshold. Since this method can provide a controllable loss term to the laser breakdown process, it is expected that a comprehensive understanding may be achieved in the future, through breakdown experiments using laser parameters with different pulse widths.
Funding
Japan Society for the Promotion of Science (JP19K21871).
Disclosures
The authors declare no conflicts of interest.
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